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Let p and q be propositions, construct the truth table for the compound proposition.
~(p^q)
Show that the series , ∞Σ n=1 (x/1+n^2x^2) is uniformly convergent in [ k,1] for any k>0.
A property agent wants to determine the effect of house sizes on sales prices. He has randomly selected 10 houses for the study. The size of houses (square feet) and sales prices ($'000) were recorded as follows.
No. 1 2 3 4 5 6 7 8 9 10
House Size (square feet) 1002-1252-1270-1200-1591-1971-1182-1010-1659-1618
Sales Price ($'000) 772 - 526 - 398 - 330 - 797 - 794 - 720 - 585 - 781 - 635
i. Using MS Excel, write down the least square regression equation and interpret the regression coefficients. (7 marks)
ii. Identify coefficient of correlation and interpret its meaning. (3 marks)
iii. State and interpret coefficient of determination. (3 marks)
iv. Predict the sales price of a house with the size of 1500 square feet and comment on its reliability. (4 marks)
v. At 10% level of significance, test whether there is a linear relationship between house size and sales price. (8 marks)
Show that if A, B, and C are sets, then A ∩ B ∩ C = A ∪ B ∪ C
•by showing each side is a subset of the other side.
•using a membership table.
Venn diagram
(A ∩ B) ∪ (A ∩ C)
(A ∩ ) ∪ (A ∩ )
Mario has decided to make party baskets for the fund raiser. balloons are sold in bags of 10, and there are 8 candy bars in a package. How many of each should he buy so there are an equal number of balloons , horns , and candy bars in each basket?
Determine the equations of the tangent and normal to:
1. 𝑇ℎ𝑒 𝑝𝑎𝑟𝑎𝑏𝑜𝑙𝑎 𝑦² = 6𝑥 − 3 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑙𝑖𝑛𝑒 𝑥 + 3𝑦 = 7
2. 𝑇ℎ𝑒 𝑒𝑙𝑙𝑖𝑝𝑠𝑒 𝑥² + 2𝑦² = 9 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑡𝑜 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒 4𝑥 − 𝑦 = 6
3. 𝑇ℎ𝑒 𝑐𝑢𝑟𝑣𝑒 (𝑥 − 𝑦) ² + 4𝑥 − 1 = 0 𝑎𝑡 (1,0)
4. 𝑇ℎ𝑒 𝑐𝑢𝑟𝑣𝑒 𝑦 = 2𝑥/𝑥+2 𝑎𝑡 𝑥 = 2
Locate the critical points and determine whether the given functions are either
maxima or minima using First Derivate Test and Second Derivative Test:
5. 𝑦 = 𝑥 ²(𝑥 − 2)²
6. 𝑦 = 𝑥(𝑥² − 6𝑥 − 15) + 50
7. 9a³y = x(4a − x)³
Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Express each of these sets with bit strings where the ith bit in the string is 1 if i is in the set and 0 otherwise.
{3, 4, 5}=0011100000
{1, 3, 6, 10} = 1010010001
{2, 3, 4, 7, 8, 9}= ?
Izzie has a muffin tin that holds 12 muffin cups. Each cup is cylindrical with a diameter of 3 and a height of 3.5 inches. Izzie has 544.28 cubic inches of batter. How many muffins did she bake?
You want to purchase a new phone that costs $475. You have $95 in savings and can save $20 per week. How many weeks will it take for you to be able to afford the new phone?
